Determination of stress-strain properties of materials and formulation of suitable constitutive laws is very important in order that: (i) the elastic-plastic response and collapse mode of structures can be analysed for improving subsequent design, and (ii) analysis of high speed metal cutting and metal forming processes may provide improved estimations of process parameters and better understanding of material flow behaviour. Numerous techniques of high strain rate testing have been reported in the literature and most require transient measurements using sophisticated and often expensive instrumentation. The main criticism of these techniques is that there is always some inherent inaccuracy present especially when measurement of transient load is involved. In recent years, a new technique was reported in which high speed photographic means were employed. The technique avoids the measurement of transit load but is very tedious and expensive. This thesis is devoted to the development and verification of a novel rate-dependent constitutive law which is capable of describing the elasto-plastic behaviour of three classes of engineering materials under dynamic loading conditions and large deformation. The materials examined were: metallic alloys (aluminium, brass, copper and steel); metal matrix composites (Al-Cu MMC and AL-Li MMC ); and a polymeric material (Nylon). Both theoretical and experimental investigations were conducted to achieve the above set objectives. In the theoretical investigations, finite difference algorithms were developed to describe the elasto-plastic behaviour of the examined materials using a novel constitutive law. The algorithms take into account the effect of inertia, interfacial friction, strain hardening and thermal softening. The experimental investigations were divided into two main sections. In the first, ballistic test experiments were conducted in conjunction with the theoretical work to evaluate the material constants needed in the newly developed constitutive law. In the second, the ballistic tests were used to verify the proposed law. In this case, both the deformation and loading history were measured and compared with the theoretical predictions. The results reveal good agreement between the two.